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Wed 26 Jul, 2006 11:26 pm
Is there Gold on the Island?
On the Isle of Truth and Lies, there live only two types of people: the
Truth-tellers, who always tell the truth; and the Liars, who always lie.
Everyone on the island fits into one of these categories.
There is a legend that there is gold on this island, but no foreigner knows for
sure. The only people who may know are those who live on the island.
Dr. Boolean--an expert at discerning truth from falsehood--decides that he will
test the legend and discover whether there is gold on the island or not.
Upon arrival on the island, he meets a man named Agg. Being a straightforward
man, Dr. Boolean asks: "Is there gold on this island?" But Agg
replies: "I once said there was." After thinking for a while, Dr.
Boolean decides that this answer was not of much help, so he continues on his
way.
A short time later, Dr. Boolean meets another man named Bagg. Again, Dr. Boolean
asks: "Is there gold on this island?" Bagg replies: "I never said
there wasn't." Again, Dr. Boolean decides this answer is not very useful,
so he decides to take a different approach with the next person he sees.
Soon, he meets a third man named Cagg. He asks: "Are Agg and Bagg of the
same type--meaning, are they both Truth-tellers or both Liars?" After Cagg
answers, Dr. Boolean thanks him and continues on with his journey.
Later, he meets a fourth man who is named Dagg. Dr. Boolean asks him: "Are
you and Cagg of the same type?" Once Dr. Boolean hears Dagg's response, he
shouts: "Eureka, I've solved the puzzle!"
So, is there gold on the island?
I'd say yes because he can't conclude that there is not gold.
Agg said, "I once said there was." If he's telling the truth, then there is gold because he would have been telling the truth when he once said there was. If he's lying, then he never said there was. We don't know if he ever said there wasn't; so there may be gold.
Bagg said, "I never said there wasn't." If he's telling the truth, then there may be gold because we don't know if he ever said there was. If he's lying, then he has said there wasn't. That would have also been a lie; so there is gold.
Based on the first two responses, he can only conclude that there is gold or there may be gold. Given that he solved the puzzle, there must be gold.
If Cagg is a truth teller and answers yes, then there is gold. If Cagg is a liar and answers no, then there is gold. Otherwise, there may be gold.
If Dagg answers yes, then Cagg is a truth teller. Otherwise, Cagg is a liar.
So, if Dagg and Cagg give the same answer, there is gold. Otherwise, there may be gold.
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